Fill hole with spherical cap
Any other way will leave a flat face. The way I do it is to create the exact size UV sphere with the same amount of segments, delete the unnecessary faces, and then manually connect the vertices to the cap of the new UV Sphere.

But I'm guessing since you have so many segments that would take forever. So another more inaccurate way- since it's a sphere is...
Extrude the opening's edge 2 or 3 times. Then merge the smallest loop into a single vertice.
From there you can adjust the height of the new vertice loops until the smooth operator or subsurface takes effect visually.